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• Find vertices of a convex hull

  - by Jeff Bullard

  I am attempting to do this within CGAL. From a 3D point cloud, find the convex hull, then loop over the finite facets of the convex hull and print each facet's vertices. It seems like there should be a straightforward way to do this; I would have expected that 3D polyhedra would own a vector of facet objects, each of which in turn would own a vector of its edges, each of which in turn would own a vector of its vertices, and that their would be some access through this hierarchy using iterators. But so far I have been unable to find a simple way to navigate through this hierarchy (if it exists).

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• Partial recalculation of visibility on a 2D uniform grid

  - by Martin Källman

  Problem Imagine that we have a 2D uniform grid of dimensions N x N. For this grid we have also pre-computed a visibility look-up table, e.g. with DDA, which answers the boolean query is cell X visible from cell Y? The look-up table is a complete graph KN of the cells V in the grid, with each edge E being a binary value denoting the visibility between its vertices. Question If any given cell has its visibility modified, is it possible to extract the subset Edelta of edges which must have their visibility recomputed due to the change, so as to avoid a full-on recomputation for the entire grid? (Which is N(N-1) / 2 or N2 depending on the implementation) Update If is not possible to solve thi in closed form, then maintaining a separate mapping of each cell and every cell pair who's line intersects said cell might also be an option. This obviously consumes more memory, but the data is static. The increased memory requirement could be reduced by introducing a hierarchy, subdividing the grid into smaller parts, and by doing so the above mapping can be reused for each sub-grid. This would come at a cost in terms of increased computation relative to the number of subdivisions; also requiring a resumable ray-casting algorithm.

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• Applying effects to an existing program that uses BasicEffect

  - by Fibericon

  Using the finished product from the tutorial here. Is it possible to apply the grayscale effect from here: Making entire scene fade to grayscale Or would you basically have to rewrite everything? EDIT: It's doing something now, but the whole grayscale seems extremely blue. It's like I'm looking at it through dark blue sunglasses. Here's my draw function: protected override void Draw(GameTime gameTime) { device.SetRenderTarget(renderTarget); graphics.GraphicsDevice.Clear(Color.CornflowerBlue); //Drawing models, bullets, etc. device.SetRenderTarget(null); spriteBatch.Begin(0, BlendState.Additive, SamplerState.PointWrap, DepthStencilState.Default, RasterizerState.CullNone, grayScale); Texture2D temp = (Texture2D)renderTarget; grayScale.Parameters["coloredTexture"].SetValue(temp); grayScale.CurrentTechnique = grayScale.Techniques["Grayscale"]; foreach (EffectPass pass in grayScale.CurrentTechnique.Passes) { pass.Apply(); } spriteBatch.Draw(temp, new Vector2(GraphicsDevice.PresentationParameters.BackBufferWidth/2, GraphicsDevice.PresentationParameters.BackBufferHeight/2), null, Color.White, 0f, new Vector2(renderTarget.Width/2, renderTarget.Height/2), 1.0f, SpriteEffects.None, 0f); spriteBatch.End(); base.Draw(gameTime); } Another edit: figured out what I was doing wrong. I have Blendstate.Additive in the spriteBatch.Draw() call. It should be Blendstate.Opaque, or it literally tries to add the blank blue image to the grayscale image.

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• How to limit click'n'drag movement to an area?

  - by Vexille

  I apologize for the somewhat generic title. I'm really don't have much clue about how to accomplish what I'm trying to do, which is making it harder even to research a possible solution. I'm trying to implement a path marker of sorts (maybe there's a most suitable name for it, but this is the best I could come up with). In front of the player there will be a path marker, which will determine how the player will move once he finishes planning his turn. The player may click and drag the marker to the position they choose, but the marker can only be moved within a defined working area (the gray bit). So I'm now stuck with two problems: First of all, how exactly should I define that workable area? I can imagine maybe two vectors that have the player as a starting point to form the workable angle, and maybe those two arcs could come from circles that have their center where the player is, but I definetly don't know how to put this all together. And secondly, after I've defined the area where the marker can be placed, how can I enforce that the marker should only stay within that area? For example, if the player clicks and drags the marker around, it may move freely within the working area, but must not leave the boundaries of the area. So for example, if the player starts dragging the marker upwards, it will move upwards until it hits he end of the working area (first diagram below), but if after that the player starts dragging sideways, the marker must follow the drag while still within the area (second diagram below). I hope this wasn't all too confusing. Thanks, guys.

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• 2D metaball liquid effect - how to feed output of one rendering pass as input to another shader

  - by Guye Incognito

  I'm attempting to make a shader for unity3d web project. I want to implement something like in the great answer by DMGregory in this question. in order to achieve a final look something like this.. Its metaballs with specular and shading. The steps to make this shader are. 1. Convert the feathered blobs into a heightmap. 2. Generate a normalmap from the heightmap 3. Feed the normal map and height map into a standard unity shader, for instance transparent parallax specular. I pretty much have all the pieces I need assembled but I am new to shaders and need help putting them together I can generate a heightmap from the blobs using some fragment shader code I wrote (I'm just using the red channel here cus i dont know if you can access the brightness) half4 frag (v2f i) : COLOR{ half4 texcol,finalColor; texcol = tex2D (_MainTex, i.uv); finalColor=_MyColor; if(texcol.r<_botmcut) { finalColor.r= 0; } else if((texcol.r>_topcut)) { finalColor.r= 0; } else { float r = _topcut-_botmcut; float xpos = _topcut - texcol.r; finalColor.r= (_botmcut + sqrt((xpos*xpos)-(r*r)))/_constant; } return finalColor; } turns these blobs.. into this heightmap Also I've found some CG code that generates a normal map from a height map. The bit of code that makes the normal map from finite differences is here void surf (Input IN, inout SurfaceOutput o) { o.Albedo = fixed3(0.5); float3 normal = UnpackNormal(tex2D(_BumpMap, IN.uv_MainTex)); float me = tex2D(_HeightMap,IN.uv_MainTex).x; float n = tex2D(_HeightMap,float2(IN.uv_MainTex.x,IN.uv_MainTex.y+1.0/_HeightmapDimY)).x; float s = tex2D(_HeightMap,float2(IN.uv_MainTex.x,IN.uv_MainTex.y-1.0/_HeightmapDimY)).x; float e = tex2D(_HeightMap,float2(IN.uv_MainTex.x-1.0/_HeightmapDimX,IN.uv_MainTex.y)).x; float w = tex2D(_HeightMap,float2(IN.uv_MainTex.x+1.0/_HeightmapDimX,IN.uv_MainTex.y)).x; float3 norm = normal; float3 temp = norm; //a temporary vector that is not parallel to norm if(norm.x==1) temp.y+=0.5; else temp.x+=0.5; //form a basis with norm being one of the axes: float3 perp1 = normalize(cross(norm,temp)); float3 perp2 = normalize(cross(norm,perp1)); //use the basis to move the normal in its own space by the offset float3 normalOffset = -_HeightmapStrength * ( ( (n-me) - (s-me) ) * perp1 + ( ( e - me ) - ( w - me ) ) * perp2 ); norm += normalOffset; norm = normalize(norm); o.Normal = norm; } Also here is the built-in transparent parallax specular shader for unity. Shader "Transparent/Parallax Specular" { Properties { _Color ("Main Color", Color) = (1,1,1,1) _SpecColor ("Specular Color", Color) = (0.5, 0.5, 0.5, 0) _Shininess ("Shininess", Range (0.01, 1)) = 0.078125 _Parallax ("Height", Range (0.005, 0.08)) = 0.02 _MainTex ("Base (RGB) TransGloss (A)", 2D) = "white" {} _BumpMap ("Normalmap", 2D) = "bump" {} _ParallaxMap ("Heightmap (A)", 2D) = "black" {} } SubShader { Tags {"Queue"="Transparent" "IgnoreProjector"="True" "RenderType"="Transparent"} LOD 600 CGPROGRAM #pragma surface surf BlinnPhong alpha #pragma exclude_renderers flash sampler2D _MainTex; sampler2D _BumpMap; sampler2D _ParallaxMap; fixed4 _Color; half _Shininess; float _Parallax; struct Input { float2 uv_MainTex; float2 uv_BumpMap; float3 viewDir; }; void surf (Input IN, inout SurfaceOutput o) { half h = tex2D (_ParallaxMap, IN.uv_BumpMap).w; float2 offset = ParallaxOffset (h, _Parallax, IN.viewDir); IN.uv_MainTex += offset; IN.uv_BumpMap += offset; fixed4 tex = tex2D(_MainTex, IN.uv_MainTex); o.Albedo = tex.rgb * _Color.rgb; o.Gloss = tex.a; o.Alpha = tex.a * _Color.a; o.Specular = _Shininess; o.Normal = UnpackNormal(tex2D(_BumpMap, IN.uv_BumpMap)); } ENDCG } FallBack "Transparent/Bumped Specular" }

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• Splitting Graph into distinct polygons in O(E) complexity

  - by Arthur Wulf White

  If you have seen my last question: trapped inside a Graph : Find paths along edges that do not cross any edges How do you split an entire graph into distinct shapes 'trapped' inside the graph(like the ones described in my last question) with good complexity? What I am doing now is iterating over all edges and then starting to traverse while always taking the rightmost turn. This does split the graph into distinct shapes. Then I eliminate all the excess shapes (that are repeats of previous shapes) and return the result. The complexity of this algorithm is O(E^2). I am wondering if I could do it in O(E) by removing edges I already traversed previously. My current implementation of that returns unexpected results.

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• Robust line of sight test on the inside of a polygon with tolerance

  - by David Gouveia

  Foreword This is a followup to this question and the main problem I'm trying to solve. My current solution is an hack which involves inflating the polygon, and doing most calculations on the inflated polygon instead. My goal is to remove this step completely, and correctly solve the problem with calculations only. Problem Given a concave polygon and treating all of its edges as if they were walls in a level, determine whether two points A and B are in line of sight of each other, while accounting for some degree of floating point errors. I'm currently basing my solution on a series of line-segment interection tests. In other words: If any of the end points are outside the polygon, they are not in line of sight. If both end points are inside the polygon, and the line segment from A to B crosses any of the edges from the polygon, then they are not in line of sight. If both end points are inside the polygon, and the line segment from A to B does not cross any of the edges from the polygon, then they are in line of sight. But the problem is dealing correctly with all the edge cases. In particular, it must be able to deal with all the situations depicted below, where red lines are examples that should be rejected, and green lines are examples that should be accepted. I probably missed a few other situations, such as when the line segment from A to B is colinear with an edge, but one of the end points is outside the polygon. One point of particular interest is the difference between 1 and 9. In both cases, both end points are vertices of the polygon, and there are no edges being intersected, but 1 should be rejected while 9 should be accepted. How to distinguish these two? I could check some middle point within the segment to see if it falls inside or not, but it's easy to come up with situations in which it would fail. Point 7 was also pretty tricky and I had to to treat it as a special case, which checks if two points are adjacent vertices of the polygon directly. But there are also other chances of line segments being col linear with the edges of the polygon, and I'm still not entirely sure how I should handle those cases. Is there any well known solution to this problem?

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• Transforming a primitive tetrahedron into a primitive icosahedron?

  - by Djentleman

  I've created a tetrahedron by creating a BoundingBox and building the faces of the tetrahedron within the bounding box as follows (see image as well): VertexPositionNormalTexture[] vertices = new VertexPositionNormalTexture[12]; BoundingBox box = new BoundingBox(new Vector3(-1f, 1f, 1f), new Vector3(1f, -1f, -1f)); vertices[0].Position = box.GetCorners()[0]; vertices[1].Position = box.GetCorners()[2]; vertices[2].Position = box.GetCorners()[7]; vertices[3].Position = box.GetCorners()[0]; vertices[4].Position = box.GetCorners()[5]; vertices[5].Position = box.GetCorners()[2]; vertices[6].Position = box.GetCorners()[5]; vertices[7].Position = box.GetCorners()[7]; vertices[8].Position = box.GetCorners()[2]; vertices[9].Position = box.GetCorners()[5]; vertices[10].Position = box.GetCorners()[0]; vertices[11].Position = box.GetCorners()[7]; What would I then have to do to transform this tetrahedron into an icosahedron? Similar to this image: I understand the concept but applying it is another thing entirely for me.

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• Convex Hull for Concave Objects

  - by Lighthink

  I want to implement GJK and I want it to handle concave shapes too (almost all my shapes are concave). I've thought of decomposing the concave shape into convex shapes and then building a hierarchical tree out of convex shapes, but I do not know how to do it. Nothing I could find on the Internet about it wasn't satisfying my needs, so maybe someone can point me in the right direction or give a full explanation.

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• Scanline filling of polygons that share edges and vertices

  - by Belgin

  In this picture (a perspective projection of an icosahedron), the scanline (red) intersects that vertex at the top. In an icosahedron each edge belongs to two triangles. From edge a, only one triangle is visible, the other one is in the back. Same for edge d. Also, in order to determine what color the current pixel should be, each polygon has a flag which can either be 'in' or 'out', depending upon where on the scanline we currently are. Flags are flipped according to the intersection of the scanline with the edges. Now, as we go from a to d (because all edges are intersected with the scanline at that vertex), this happens: the triangle behind triangle 1 and triangle 1 itself are set 'in', then 2 is set in and 1 is 'out', then 3 is set 'in', 2 is 'out' and finally 3 is 'out' and the one behind it is set 'in', which is not the desired behavior because we only need the triangles which are facing us to be set 'in', the rest should be 'out'. How do process the edges in the Active Edge List (a list of edges that are currently intersected by the scanline) so the right polys are set 'in'? Also, I should mention that the edges are unique, which means there exists an array of edges in the data structure of the icosahedron which are pointed to by edge pointers in each of the triangles.

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• Best way to detect if vec3 is between vec3(x) and vec3(y) in glsl

  - by elect

  As titled I am sampling from a texture and if the color is somehow gray [vec3(.8), vec3(.9)] and an uniform is 1 I need to substitute that color with another one I am not a glsl veteran but I am pretty sure there is a more elegant and compact (without mentioning faster) way than this: vec3 textureColor = texture(texture0, oUV); if(settings.w == 1 && textureColor.r > .8 && textureColor.r < .9 && textureColor.g > .8 && textureColor.g < .9 && textureColor.b > .8 && textureColor.b < .9)

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• Annoying flickering of vertices and edges (possible z-fighting)

  - by Belgin

  I'm trying to make a software z-buffer implementation, however, after I generate the z-buffer and proceed with the vertex culling, I get pretty severe discrepancies between the vertex depth and the depth of the buffer at their projected coordinates on the screen (i.e. zbuffer[v.xp][v.yp] != v.z, where xp and yp are the projected x and y coordinates of the vertex v), sometimes by a small fraction of a unit and sometimes by 2 or 3 units. Here's what I think is happening: Each triangle's data structure holds the plane's (that is defined by the triangle) coefficients (a, b, c, d) computed from its three vertices from their normal: void computeNormal(Vertex *v1, Vertex *v2, Vertex *v3, double *a, double *b, double *c) { double a1 = v1 -> x - v2 -> x; double a2 = v1 -> y - v2 -> y; double a3 = v1 -> z - v2 -> z; double b1 = v3 -> x - v2 -> x; double b2 = v3 -> y - v2 -> y; double b3 = v3 -> z - v2 -> z; *a = a2*b3 - a3*b2; *b = -(a1*b3 - a3*b1); *c = a1*b2 - a2*b1; } void computePlane(Poly *p) { double x = p -> verts[0] -> x; double y = p -> verts[0] -> y; double z = p -> verts[0] -> z; computeNormal(p -> verts[0], p -> verts[1], p -> verts[2], &p -> a, &p -> b, &p -> c); p -> d = p -> a * x + p -> b * y + p -> c * z; } The z-buffer just holds the smallest depth at the respective xy coordinate by somewhat casting rays to the polygon (I haven't quite got interpolation right yet so I'm using this slower method until I do) and determining the z coordinate from the reversed perspective projection formulas (which I got from here: double z = -(b*Ez*y + a*Ez*x - d*Ez)/(b*y + a*x + c*Ez - b*Ey - a*Ex); Where x and y are the pixel's coordinates on the screen; a, b, c, and d are the planes coefficients; Ex, Ey, and Ez are the eye's (camera's) coordinates. This last formula does not accurately give the exact vertices' z coordinate at their projected x and y coordinates on the screen, probably because of some floating point inaccuracy (i.e. I've seen it return something like 3.001 when the vertex's z-coordinate was actually 2.998). Here is the portion of code that hides the vertices that shouldn't be visible: for(i = 0; i < shape.nverts; ++i) { double dist = shape.verts[i].z; if(z_buffer[shape.verts[i].yp][shape.verts[i].xp].z < dist) shape.verts[i].visible = 0; else shape.verts[i].visible = 1; } How do I solve this issue? EDIT I've implemented the near and far planes of the frustum, with 24 bit accuracy, and now I have some questions: Is this what I have to do this in order to resolve the flickering? When I compare the z value of the vertex with the z value in the buffer, do I have to convert the z value of the vertex to z' using the formula, or do I convert the value in the buffer back to the original z, and how do I do that? What are some decent values for near and far? Thanks in advance.

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• simple collision detection

  - by Rob

  Imagine 2 squares sitting side by side, both level with the ground: http://img19.imageshack.us/img19/8085/sqaures2.jpg A simple way to detect if one is hitting the other is to compare the location of each side. They are touching if ALL of the following are NOT true: The right square's left side is to the right of the left square's right side. The right square's right side is to the left of the left square's left side. The right square's bottom side is above the left square's top side. The right square's top side is below the left square's bottom side. If any of those are true, the squares are not touching. If all of those are false, the squares are touching. But consider a case like this, where one square is at a 45 degree angle: http://img189.imageshack.us/img189/4236/squaresb.jpg Is there an equally simple way to determine if those squares are touching?

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• Intersection points of plane set forming convex hull

  - by Toji

  Mostly looking for a nudge in the right direction here. Given a set of planes (defined as a normal and distance from origin) that form a convex hull, I would like to find the intersection points that form the corners of that hull. More directly, I'm looking for a way to generate a point cloud appropriate to provide to Bullet. Bonus points if someone knows of a way I could give bullet the plane list directly, since I somewhat suspect that's what it's building on the backend anyway.

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• Circle-Line Collision Detection Problem

  - by jazzdawg

  I am currently developing a breakout clone and I have hit a roadblock in getting collision detection between a ball (circle) and a brick (convex polygon) working correctly. I am using a Circle-Line collision detection test where each line represents and edge on the convex polygon brick. For the majority of the time the Circle-Line test works properly and the points of collision are resolved correctly. Collision detection working correctly. However, occasionally my collision detection code returns false due to a negative discriminant when the ball is actually intersecting the brick. Collision detection failing. I am aware of the inefficiency with this method and I am using axis aligned bounding boxes to cut down on the number of bricks tested. My main concern is if there are any mathematical bugs in my code below. /* * from and to are points at the start and end of the convex polygons edge. * This function is called for every edge in the convex polygon until a * collision is detected. */ bool circleLineCollision(Vec2f from, Vec2f to) { Vec2f lFrom, lTo, lLine; Vec2f line, normal; Vec2f intersectPt1, intersectPt2; float a, b, c, disc, sqrt_disc, u, v, nn, vn; bool one = false, two = false; // set line vectors lFrom = from - ball.circle.centre; // localised lTo = to - ball.circle.centre; // localised lLine = lFrom - lTo; // localised line = from - to; // calculate a, b & c values a = lLine.dot(lLine); b = 2 * (lLine.dot(lFrom)); c = (lFrom.dot(lFrom)) - (ball.circle.radius * ball.circle.radius); // discriminant disc = (b * b) - (4 * a * c); if (disc < 0.0f) { // no intersections return false; } else if (disc == 0.0f) { // one intersection u = -b / (2 * a); intersectPt1 = from + (lLine.scale(u)); one = pointOnLine(intersectPt1, from, to); if (!one) return false; return true; } else { // two intersections sqrt_disc = sqrt(disc); u = (-b + sqrt_disc) / (2 * a); v = (-b - sqrt_disc) / (2 * a); intersectPt1 = from + (lLine.scale(u)); intersectPt2 = from + (lLine.scale(v)); one = pointOnLine(intersectPt1, from, to); two = pointOnLine(intersectPt2, from, to); if (!one && !two) return false; return true; } } bool pointOnLine(Vec2f p, Vec2f from, Vec2f to) { if (p.x >= min(from.x, to.x) && p.x <= max(from.x, to.x) && p.y >= min(from.y, to.y) && p.y <= max(from.y, to.y)) return true; return false; }

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• Wrong faces culled in OpenGL when drawing a rectangular prism

  - by BadSniper

  I'm trying to learn opengl. I did some code for building a rectangular prism. I don't want to draw back faces so I used glCullFace(GL_BACK), glEnable(GL_CULL_FACE);. But I keep getting back faces also when viewing from front and also sometimes when rotating sides are vanishing. Can someone point me in right direction? glPolygonMode(GL_FRONT,GL_LINE); // draw wireframe polygons glColor3f(0,1,0); // set color green glCullFace(GL_BACK); // don't draw back faces glEnable(GL_CULL_FACE); // don't draw back faces glTranslatef(-10, 1, 0); // position glBegin(GL_QUADS); // face 1 glVertex3f(0,-1,0); glVertex3f(0,-1,2); glVertex3f(2,-1,2); glVertex3f(2,-1,0); // face 2 glVertex3f(2,-1,2); glVertex3f(2,-1,0); glVertex3f(2,5,0); glVertex3f(2,5,2); // face 3 glVertex3f(0,5,0); glVertex3f(0,5,2); glVertex3f(2,5,2); glVertex3f(2,5,0); // face 4 glVertex3f(0,-1,2); glVertex3f(2,-1,2); glVertex3f(2,5,2); glVertex3f(0,5,2); // face 5 glVertex3f(0,-1,2); glVertex3f(0,-1,0); glVertex3f(0,5,0); glVertex3f(0,5,2); // face 6 glVertex3f(0,-1,0); glVertex3f(2,-1,0); glVertex3f(2,5,0); glVertex3f(0,5,0); glEnd();

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• How do I pass an object location into a vertex shader?

  - by Greg Kassapidis

  I am using Blender Game Engine. I want to create a large flat plane, and deform it locally near a moving object. So far (despite being a beginner at shaders) I've written a vertex shader for the plane which moves the vertices to their correct positions (constant positions, for now). I cannot find a way to swap that constant location with an object's location updated every frame, while the shader is running. I am not even sure if it's possible. I only want to access a specific object's center from the shader.

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• "Walking" along a rotating surface in LimeJS

  - by Dave Lancea

  I'm trying to have a character walk along a plank (a long, thin rectangle) that works like a seesaw, being rotated around a central point by box2d physics (falling objects). I want the left and right arrow keys to move the player up and down the plank, regardless of it's slope, and I don't want to use real physics for the player movement. My idea for achieving this was to compute the coordinate based on the rotation of the plank and the current location "up" or "down" the board. My math is derived from here: http://math.stackexchange.com/questions/143932/calculate-point-given-x-y-angle-and-distance Here's the code I have so far: movement = 0; if(keys[37]){ // Left movement = -3; } if(keys[39]){ // Right movement = 3; } // this.plank is a LimeJS sprite. // getRotation() Should return an angle in degrees var rotation = this.plank.getRotation(); // this.current_plank_location is initialized as 0 this.current_plank_location += movement; var x_difference = this.current_plank_location * Math.cos(rotation); var y_difference = this.current_plank_location * Math.sin(rotation); this.setPosition(seesaw.PLANK_CENTER_X + x_difference, seesaw.PLANK_CENTER_Y + y_difference); This code causes the player to swing around in a circle when they are out of the center of the plank given a slight change in rotation of the plank. Any ideas on how I can get the player position to follow the board position?

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• Algorithm to calculate trajectories from vector field

  - by cheeesus

  I have a two-dimensional vector field, i.e., for each point (x, y) I have a vector (u, v), whereas u and v are functions of x and y. This vector field canonically defines a set of trajectories, i.e. a set of paths a particle would take if it follows along the vector field. In the following image, the vector field is depicted in red, and there are four trajectories which are partly visible, depicted in dark red: I need an algorithm which efficiently calculates some trajectories for a given vector field. The trajectories must satisfy some kind of minimum denseness in the plane (for every point in the plane we must have a 'nearby' trajectory), or some other condition to get a reasonable set of trajectories. I could not find anything useful on Google on this, and Stackexchange doesn't seem to handle the topic either. Before I start devising such an algorithm by myself: Are there any known algorithms for this problem? What is their name, for which keywords do I have to search?

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• Adding tolerance to a point in polygon test

  - by David Gouveia

  I've been using this method which was taken from Game Coding Complete to detect whether a point is inside of a polygon. It works in almost every case, but is failing on a few edge cases, and I can't figure out the reason. For example, given a polygon with vertices at (0,0) (0,100) and (100,100), the algorithm is returning: True for any point strictly inside the polygon False for any of the vertices False for (0, 50) which lies on one of the edges of the polygon True (?) for (50,50) which is also on one of the edges of the polygon I'd actually like to relax the algorithm so that it returns true in all of these cases. In other words, it should return true for points that are strictly inside, for the vertices themselves, and for points on the edges of the polygon. If possible I'd also like to give it enough tolerance so that it always tend towards "true" in face of floating point fluctuations. For example, I have another method, that given a line segment and a point, returns the closest location on the line segment to the given point. Currently, given any point outside the polygon and one of its edges, there are cases where the result is categorized as being inside by the method above, while other points are considered outside. I'd like to give it enough tolerance so that it always returns true in this situation. The way I've currently solved the problem is an hack, which consists of using an external library to inflate the polygon by a few pixels, and performing the tests on the inflated polygon, but I'd really like to replace this with a proper solution.

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• Fast software color interpolating triangle rasterization technique

  - by Belgin

  I'm implementing a software renderer with this rasterization method, however, I was wondering if there is a possibility to improve it, or if there exists an alternative technique that is much faster. I'm specifically interested in rendering small triangles, like the ones from this 100k poly dragon: As you can see, the method I'm using is not perfect either, as it leaves small gaps from time to time (at least I think that's what's happening). I don't mind using assembly optimizations. Pseudocode or actual code (C/C++ or similar) is appreciated. Thanks in advance.

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• How to perform simple collision detection?

  - by Rob

  Imagine two squares sitting side by side, both level with the ground like so: A simple way to detect if one is hitting the other is to compare the location of each side. They are touching if all of the following are false: The right square's left side is to the right of the left square's right side. The right square's right side is to the left of the left square's left side. The right square's bottom side is above the left square's top side. The right square's top side is below the left square's bottom side. If any of those are true, the squares are not touching. But consider a case like this, where one square is at a 45 degree angle: Is there an equally simple way to determine if those squares are touching?

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• exact point oh a rotating sphere

  - by nkint

  I have a sphere that represents the heart textured with real pictures. It's rotating about the x axis, and when user click down it has to show me the exact place he clicked on. For example if he clicked on Singapore and the system should be able to: understand that user clicked on the sphere (OK, I'll do it with unProject) understand where user clicked on the sphere (ray-sphere collision?) and take into account the rotation transform sphere-coordinate to some coordinate system good for some web-api service ask to api (OK, this is the simpler thing for me ;-) some advice?

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• Repairing back-facing triangles without user input

  - by LTR

  My 3D application works with user-imported 3D models. Frequently, those models have a few vertices facing into the wrong direction. (For example, there is a 3D roof and a few triangles of that roof are facing inside the building). I want to repair those automatically. We can make several assumptions about these 3D models: they are completely closed without holes, and the camera is always on the outside. My idea: Shoot 500 rays from every triangle outwards into all directions. From the back side of the triangle, all rays will hit another part of the model. From the front side, at least one ray will hit nothing. Is there a better algorithm? Are there any papers about something like this?

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• using heightmap to simulate 3d in an isometric 2d game

  - by VaTTeRGeR

  I saw a video of an 2.5d engine that used heightmaps to do zbuffering. Is this hard to do? I have more or less no idea of Opengl(lwjgl) and that stuff. I could imagine, that you compare each pixel and its depthmap to the depthmap of the already drawn background to determine if it gets drawn or not. Are there any tutorials on how to do this, is this a common problem? It would already be awesome if somebody knows the names of the Opengl commands so that i can go through some general tutorials on that. greets! Great 2.5d engine with the needed effect, pls go to the last 30 seconds Edit, just realised, that my question wasn't quite clear expressed: How can i tell Opengl to compare the existing depthbuffer with an grayscale texure, to determine if a pixel should get drawn or not?

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